If particles cannot move faster than light then points of a wave function must be discontinuous in time and distance. Because, all near points where a particle has a non-zero probability of existence must be far enough apart in time and distance so that a particle cannot break the speed of light by tunneling. Deferential equations do not give such solutions.
No, well-known math is necessary and sufficient. The statements about the wavefunction are, simply, wrong and the correct statements are in any textbook on quantum mechanics.
Tunneling doesn't have anything to do with the speed of light.
A quantum particle-relativistic or not-doesn't tunnel through a potential barrier-that only exists for a classical particle; its properties are consistent with a totally different potential. How to do the corresponding calculations is known.
The assumption of faster than light tunneling
is wrong, though tunneling time is a bit controversial.
So far you cannot go beyond the usual QM formalism for such situation.
Both height and width of the barrier is involved, to estimate some transmission coeficient.
If you cross something there must be a velocity the near world sees. In the gap the wave function must be zero. Schrodinger's equation only gives continuous solutions that will not be zero in the gap and non-zero on either side. When a an electron passes NEAR a standing wave it gives it some of its kinetic energy. Just what velocity does wave at 2 gap lengths from the gap. Uncertainties in position and time require knowing momentum and energy which require velocity which will be different an each side of the gap. Tunnel diodes have a negative resistance at some voltage range.
The solutions by Schrodinger's equation would 3 a wave functions zero in the gap. The gap surface therefore would be reflectors for the solution on each side of the gap. On each side of the gap it would take the form B(t,x,y,z)-B(t,,x,y,-z) where z is normal to gap wall, and B is a function.
The point about Q tunneling, is that something gets through something that would act as a effective Classical barrier. Therefore there is wave function in the gap, and there should be.
- Juan Weisz
- Suggest: You assume zero for the barrier. The solution for the input side should give a higher probability of existing in it than the output side solution for the wave function. Their ratio tells you how much crossed the barrier (gap). I have no way to know how fast tunneling goes. There is no perfect barrier, there will be some current by conventional (non-tunneling). All quantum mechanics says is that there is a non-zero probability of existing on the output side.
If you have only one particle the solutions will tell how likely it is likely to be on a side. If have 10,000 it give you how much is one each side.
I mean a bona fide Classical barrier exhibiting a usual classical turning point,
where a potential barrier is higher than the kinetic energy of some trapped particle. What, are you pretending Q tunneling does not exist?
Well, I admit that the speed is not that well defined, uncertainty principle.
You cannot inject your classical ideas very much in this.
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